Question: The grades on a chemistry midterm at Loyola are normally distributed with $\mu = 71$ and $\sigma = 3.0$. Vanessa earned a $69$ on the exam. Find the z-score for Vanessa's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Vanessa's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{69 - {71}}{{3.0}}} $ ${ z \approx -0.67}$ The z-score is $-0.67$. In other words, Vanessa's score was $0.67$ standard deviations below the mean.